Question

The slope on a distance-time graph shows a ball moving from 20 m to 40 m in 1 s and from 40 m to 80 m in the next second

Answer 1

The ball is accelerating

Explanation:

On a distance-time graph, the slope of the graph represents the speed of the object represented.

Let's therefore calculate the slope (so, the speed of the ball) in the two intervals given.

In the first second, we have:

$\Delta y = 40 - 20 = 20 m\\\Delta x = 1 s$

So the average speed is

$v_1 = \frac{\Delta y}{\Delta x}=\frac{20}{1}=20 m/s$

In the next second, we have:

$\Delta y = 80 - 40 = 40 m\\\Delta x = 1 s$

So the average speed is

$v_2 = \frac{\Delta y}{\Delta x}=\frac{40}{1}=40 m/s$

We notice that the speed of the ball has increased from 20 m/s in the first second to 40 m/s in the next second: this means that the speed of the ball is increasing, and therefore, the ball is accelerating.

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